-
Notifications
You must be signed in to change notification settings - Fork 1
/
toy_density_estimation.py
266 lines (250 loc) · 8.44 KB
/
toy_density_estimation.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
# Copyright © 2021 Dar Gilboa, Ari Pakman and Thibault Vatter
# This file is part of the mdma library and licensed under the terms of the MIT license.
# For a copy, see the LICENSE file in the root directory.
import matplotlib.pyplot as plt
import numpy as np
import torch as t
import mdma.fit as fit
import mdma.utils as utils
save_plots = True
h = fit.get_default_h()
M = 200000
save_dir = "./"
# generate data
rng = np.random.RandomState()
if h.dataset == 'gaussians':
scale = 4.
centers = [[1, 0, -1], [-1, 0, .14], [0, 1, -.43], [0, -1, .71],
[1. / np.sqrt(2), 1. / np.sqrt(2), -.71],
[1. / np.sqrt(2), -1. / np.sqrt(2), 1],
[-1. / np.sqrt(2), 1. / np.sqrt(2), -.14],
[-1. / np.sqrt(2), -1. / np.sqrt(2), .43]]
centers = scale * np.array(centers)
dataset = []
for i in range(M):
point = rng.randn(3) * 0.5
idx = rng.randint(8)
center = centers[idx]
point += center
dataset.append(point)
dataset = np.array(dataset, dtype='float32')
dataset /= 1.414
zlim = [-4, 4]
elif h.dataset == 'spirals':
n = np.sqrt(np.random.rand(M // 2, 1)) * 540 * (2 * np.pi) / 360
d1x = -np.cos(n) * n + np.random.rand(M // 2, 1) * 0.5
d1y = np.sin(n) * n + np.random.rand(M // 2, 1) * 0.5
z = np.expand_dims(np.linalg.norm(np.hstack((d1x, d1y)), axis=1), -1) / 3
dataset = np.vstack((np.hstack((d1x, d1y, z)), np.hstack(
(-d1x, -d1y, -z)))) / 3
dataset += np.random.randn(*dataset.shape) * 0.1
zlim = [-2, 2]
np.random.shuffle(dataset)
elif h.dataset == 'checkerboard':
x = np.random.rand(M)
dataset = np.zeros((M, 3))
one_centers = [.125, .625]
two_centers = [.375, .875]
one_inds = np.where((x < .25) | ((x > .5) & (x < .75)))[0]
two_inds = np.where((x > .75) | ((x > .25) & (x < .5)))[0]
dataset[:, 0] = x
for ind in [1, 2]:
dataset[one_inds, ind] = np.take(one_centers,
np.random.choice([0, 1], len(one_inds)))
dataset[two_inds, ind] = np.take(two_centers,
np.random.choice([0, 1], len(two_inds)))
dataset[:, ind] += np.random.rand(M) / 4 - .125
dataset = dataset * 8 - 4
zlim = [-4, 4]
# Plot data 3d scatter
plt.figure()
n_pts_to_plot = 2000
ax = plt.axes(projection='3d')
lenX = len(dataset)
ax.scatter3D(dataset[:n_pts_to_plot, 0],
dataset[:n_pts_to_plot, 1],
dataset[:n_pts_to_plot, 2],
s=1)
if h.dataset == 'gaussians':
ax.view_init(elev=30., azim=55)
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=90)
elif h.dataset == 'spirals':
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=90)
ax.view_init(elev=20., azim=10)
else:
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=270)
ax.set_xlabel('$x_1$', labelpad=-12)
ax.set_ylabel('$x_2$', labelpad=-12)
ax.set_title('Training data')
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])
plt.locator_params(nbins=3)
if save_plots:
plt.savefig(save_dir + '_'.join(['3d', h.dataset, 'data']) + '.pdf')
plt.show()
# Plot 2d histogram of data
ub = 4
lb = -4
grid_res = 60
lims = [[lb, ub], [lb, ub], zlim]
ax = plt.axes(projection=None)
for vars in [[0, 1], [1, 2], [0, 2]]:
hist_data = np.histogram2d(dataset[:, vars[0]],
dataset[:, vars[1]],
grid_res,
range=[lims[vars[0]], lims[vars[1]]])
lim0 = lims[vars[0]]
lim1 = lims[vars[1]]
plt.imshow(hist_data[0].transpose(),
extent=[lim0[0], lim0[1], lim1[0], lim1[1]],
aspect=(lim0[1] - lim0[0]) / (lim1[1] - lim1[0]))
plt.xlabel('$x_' + str(vars[0] + 1) + '$')
plt.ylabel('$x_' + str(vars[1] + 1) + '$')
plt.xticks([])
plt.yticks([])
plt.title('Training data')
if save_plots:
plt.savefig(save_dir + '_'.join(
['3d', h.dataset, 'data_2d',
str(vars[0] + 1),
str(vars[1] + 1)]) + '.pdf')
plt.show()
# Create model and fit
batch_size = 1000
h = fit.get_default_h()
h.batch_size = batch_size
h.d = 3
h.M = M
h.use_HT = True
if h.dataset == 'checkerboard':
h.m = 250
else:
h.m = 1000
h.model_to_load = ''
h.n_epochs = 10
h.patience = 150
h.save_checkpoints = False
loaders = utils.create_loaders([dataset, None, None], batch_size)
h.eval_validation = False
h.eval_test = False
model = fit.fit_mdma(h, loaders)
# Plot samples from model
plt.figure()
n_pts_to_plot = 2000
ax = plt.axes(projection='3d')
samples = model.sample(n_pts_to_plot)
ax.scatter3D(samples[:n_pts_to_plot, 0],
samples[:n_pts_to_plot, 1],
samples[:n_pts_to_plot, 2],
s=1)
if h.dataset == 'gaussians':
ax.view_init(elev=30., azim=55)
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=90)
elif h.dataset == 'spirals':
ax.view_init(elev=20., azim=10)
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=90)
else:
ax.zaxis.set_rotate_label(False)
ax.set_zlabel('$x_3$', labelpad=-12, rotation=270)
ax.set_title('Samples from model')
ax.set_xlabel('$x_1$', labelpad=-12)
ax.set_ylabel('$x_2$', labelpad=-12)
ax.zaxis.set_rotate_label(False)
ax.xaxis.set_ticklabels([])
ax.yaxis.set_ticklabels([])
ax.zaxis.set_ticklabels([])
plt.locator_params(nbins=3)
if save_plots:
plt.savefig(save_dir + '_'.join(['3d', h.dataset, 'model_samples_3d']) +
'.pdf')
plt.show()
# 2d marginals
lims = [[lb, ub], [lb, ub], zlim]
ax = plt.axes(projection=None)
x_coords = np.linspace(lb, ub, grid_res)
y_coords = np.linspace(lb, ub, grid_res)
z_coords = np.linspace(zlim[0], zlim[1], grid_res)
coords = [x_coords, y_coords, z_coords]
for vars in [[0, 1], [1, 2], [0, 2]]:
lim0 = lims[vars[0]]
lim1 = lims[vars[1]]
mg = np.meshgrid(coords[vars[0]], coords[vars[1]])
model_log_density = utils.eval_log_density_on_grid(model,
mg,
inds=vars,
grid_res=grid_res)
plt.figure()
plt.imshow(np.exp(model_log_density),
extent=[lim0[0], lim0[1], lim1[0], lim1[1]],
aspect=(lim0[1] - lim0[0]) / (lim1[1] - lim1[0]))
plt.xlabel('$x_' + str(vars[0] + 1) + '$')
plt.ylabel('$x_' + str(vars[1] + 1) + '$')
plt.xticks([])
plt.yticks([])
plt.title(f'$f(x_{vars[0] + 1}, x_{vars[1] + 1})$', fontsize=22)
if save_plots:
plt.savefig(save_dir + '_'.join(
['3d', h.dataset, '2d_marg',
str(vars[0] + 1),
str(vars[1] + 1)]) + '.pdf')
plt.show()
# 2d conditionals
ub = 4
lb = -4
grid_res = 60
x_coords = np.linspace(lb, ub, grid_res)
y_coords = np.linspace(lb, ub, grid_res)
mg = np.meshgrid(x_coords, y_coords)
inds = [0, 1]
cond_vals = [-.5, 0, .5]
for cond_val in cond_vals:
model_cond_density = utils.eval_cond_density_on_grid(model,
mg,
cond_val,
inds=inds,
cond_inds=[2],
grid_res=grid_res)
plt.figure(figsize=(4, 4))
plt.imshow(model_cond_density, extent=[lb, ub, lb, ub])
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.xticks([])
plt.yticks([])
plt.title('$f(x_1, x_2 | x_3 = ' + str(cond_val) + ')$', fontsize=22)
if save_plots:
plt.savefig(save_dir + '_'.join(
['3d', h.dataset, '2d_cond', str(cond_val)]) + '.pdf')
plt.show()
# 1d marginals
plt.figure(figsize=(4, 4))
if h.dataset == 'checkerboard':
rng = 5
else:
rng = 4
xs = np.linspace(-rng, rng, 100)
prop_cycle = plt.rcParams['axes.prop_cycle']
colors = prop_cycle.by_key()['color']
for i in range(3):
model_log_density = np.exp(
model.log_density(t.tensor(xs).float(), inds=[i]).cpu().detach().numpy())
plt.plot(xs, model_log_density, color=colors[i], label=f'$f(x_{i+1})$', lw=2)
hist_data = np.histogram(dataset[:, i], 100, range=(-rng, rng), density=1)
plt.plot((hist_data[1][1] - hist_data[1][0]) / 2 + hist_data[1][:-1],
hist_data[0],
'x',
color=colors[i])
plt.plot(10, 0, 'x', color='k', label='Training \n data')
plt.xlim([-rng, rng])
if h.dataset == 'gaussians':
plt.legend(handletextpad=0, handlelength=1, loc=3)
else:
plt.legend(handletextpad=0, handlelength=1)
if save_plots:
plt.savefig(save_dir + '_'.join(['3d', h.dataset, '1d_marg']) + '.pdf')
plt.show()